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Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

N000ughty Thoughts

How many noughts are at the end of these giant numbers?

Mod 3

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

Ben's Game

Age 11 to 16 Challenge Level:

Ben, Jack and Emma were playing a game with a box of $40$ counters - they were not using all of them.
They each had a small pile of counters in front of them.

Image of Ben, Jack and Emma with counters in front of them.

All at the same time, Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma, and Emma passed a fifth of her counters to Ben.

They all passed on more than one counter.

After this they all had the same number of counters.

How many could each of them have started with?



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